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Full text of "Treatise On Analysis Vol-Ii"

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NOTATION

In the following definitions, the first number is the number of the chapter and the
second number is the number of the section within that chapter.

Supp(/)                                       support of a function: 12.6

<PA                                                characteristic function of a subset A of

a set: 12.7

sup/a, inf/i                                 upper and lower envelopes of a family of

a         a                                      real-valued functions: 12.7

limsup/n, liminf/n                       upper and lower limit of a sequence of

w~*           n"                              real-valued functions: 12.7

G                                              opposite of a group G: 12.8

GL(E)                                         group of automorphisms of a topological

vector space E: 12.8

A""1                                             set of elements x~l where xe A (where

A is a subset of a group in which the
group law is written multiplicatively):
12.8

AB                                              set of elements xy with x e A and y e B,

where A and B are subsets of a group in
which the group law is written multi-
plicatively: 12.8

), ^f(H)                                normalizer and centralizer of a subset H

of a group: 12.8

set of finite products xtx2 ... xn (with n
arbitrary) of elements of a subset V of a
group: 12.8

ix
arbitrary) of elements of a subset V of a